Physics · Advanced university
Group velocity from a dispersion relation · formula reference
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
Formula
The group velocity generally differs from phase velocity ω/k; the dispersion constants carry compatible SI units.
vg = dω/dk
Worked example
A wave has dispersion ω(k)=7k + 6k³ with SI-compatible constants. Find group velocity at k=10 m⁻¹. Round the final result to 4 decimal places if needed. Answer in m/s.
Differentiate before substituting: vg=7+18k².
1807 m/s
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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